The contribution of reflections to the Lorentz-Lorenz effect

We use the static limit and delta isobar dominance to calculate the contribution to the optical potential of pionic atoms of those terms in which a pion or a rho meson are exchanged any number of times between two nucleons, which constitute the ρ² term of the Lorentz-Lorenz effect. By suppressing the spin and isospin degrees of freedom, we are able to express the Lorentz-Lorenz parameter ξ in analytical form. In the general case when we include fully the spin and isospin variables, we obtain the Lorentz-Lorenz parameter ξ in numerical form. Our results show that ξ can not be larger than one and more likely is close to zero.